We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

Pristine graphene is the strongest material ever measured. However, large-area graphene films produced by means of chemical vapor deposition (CVD) are polycrystalline and thus contain grain boundaries that can potentially weaken the material. We combined structural characterization by means of transmission electron microscopy with nanoindentation in order to study the mechanical properties of CVD-graphene films with different grain sizes. We show that the elastic stiffness of CVD-graphene is identical to that of pristine graphene if postprocessing steps avoid damage or rippling. Its strength is only slightly reduced despite the existence of grain boundaries. Indentation tests directly on grain boundaries confirm that they are almost as strong as pristine. Graphene films consisting entirely of well-stitched grain boundaries can retain ultrahigh strength, which is critical for a large variety of applications, such as flexible electronics and strengthening components.

The nonlinear in-plane elastic properties of graphene are calculated using density-functional theory. A thermodynamically rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. Upon accounting for the symmetries of graphene, a total of fourteen nonzero independent elastic constants are determined by least-squares fit to the ab initio calculations. The nonlinear continuum description is valid for infinitesimal and finite strains under arbitrary in-plane tensile loading in circumstance for which the bending stiffness can be neglected. The continuum formulation is suitable for incorporation into the finite element method.

This research explores the non-linear elastic properties of two-dimensional molybdenum disulfide. , where E is the Young's modulus. This study reveals the predictive power of first-principles density functional theory, in the derivation of non-linear elastic properties of two-dimensional MoS 2 . Furthermore, the study bridges three main gaps that hinder understanding of material properties: DFT to finite element analysis (FEA), experimental results to DFT, and the nanoscale to the microscale. In bridging these three gaps the experimental results validate the DFT calculations and the multiscale constitutive model.

Graphene is a single-atomic-layer material with excellent mechanical properties and has the potential to enhance the strength of composites. Its two-dimensional geometry, high intrinsic strength and modulus can effectively constrain dislocation motion, resulting in the significant strengthening of metals. Here we demonstrate a new material design in the form of a nanolayered composite consisting of alternating layers of metal (copper or nickel) and monolayer graphene that has ultra-high strengths of 1.5 and 4.0 GPa for copper-graphene with 70-nm repeat layer spacing and nickel-graphene with 100-nm repeat layer spacing, respectively. The ultra-high strengths of these metal-graphene nanolayered structures indicate the effectiveness of graphene in blocking dislocation propagation across the metal-graphene interface. Ex situ and in situ transmission electron microscopy compression tests and molecular dynamics simulations confirm a build-up of dislocations at the graphene interface.

We describe studies of the elastic properties and frictional characteristics of graphene samples of varying thickness using an atomic force microscope. For tensile testing, graphene is suspended over micron-sized circular holes and indented by atomic force microscope (AFM) tips. Fitting of the forcedisplacement curves yields the prestress and elastic stiffness, while comparison of the breaking force to simulation gives the ultimate strength, which is the highest measured for any material. Experiments on samples with 1-3 atomic layers yield similar values for the intrinsic stiffness and strength of a single sheet, but also reveal differences in mechanical behavior with thickness. The frictional force between an AFM tip and graphene decreases with thickness for samples from 1 to 4 layers, and does not depend on the presence of a substrate. Highresolution friction force imaging in stick-slip mode shows the same trend, and allows direct imaging of the crystal lattice.

Nanoporous metals prepared by the corrosion of an alloy can take the form of monolithic, millimeter-sized bodies containing approximately 1015 nanoscale ligaments per cubic millimeter. The ligament size can reach down to the very limits of stability of nanoscale objects. The processes by which nanoporous metals are formed have continued to be fascinating, even though their study in relation to surface treatment, metal refinement, and failure mechanisms can be traced back to ancient times. In fact, the prospect of using alloy corrosion as a means of making nanomaterials for fundamental studies and functional applications has led to a revived interest in the process. The quite distinct mechanical properties of nanoporous metals are one of the focus points of this interest, as relevant studies probe the deformation behavior of crystals at the lower end of the size scale. Furthermore, the coupling of bulk stress and strain to the forces acting along the surface of nanoporous metals provide unique opportunities for controlling the mechanical behavior through external variables such as the electrical or chemical potentials.

In monolayer transition metal dichalcogenides, quantum emitters are associated with localized strain that can be deterministically applied to create designer nano-arrays of single photon sources. Despite an overwhelming empirical correlation with local strain, the nanoscale interplay between strain, excitons, defects and local crystalline structure that gives rise to these quantum emitters is poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopy of excitons in nanobubbles of localized strain in monolayer WSe2 with atomistic structural models to elucidate how strain induces nanoscale confinement potentials that give rise to highly localized exciton states in 2D semiconductors. Nano-optical imaging of nanobubbles in low-defect monolayers reveal localized excitons on length scales of ~10 nm at multiple sites along the periphery of individual nanobubbles, which is in stark contrast to predictions of continuum models of strain. These results agree with theoretical confinement potentials that are atomistically derived from measured topographies of existing nanobubbles. Our results provide one-of-a-kind experimental and theoretical insight of how strain-induced confinement-without crystalline defects-can efficiently localize excitons on length scales commensurate with exciton size, providing key nanoscale structure-property information for quantum emitter phenomena in monolayer WSe2.The intense light-matter interactions of two-dimensional (2D) monolayer transition metal dichalcogenides (1L-TMDs) are mediated by a diverse suite of excitonic phenomena that present a wealth of opportunities for novel optoelectronic functionalities in areas spanning from high- *